ORLANDO, Fla. — Rick Perry and Mitt Romney played a rhetorical badminton game in the debate here Thursday, with the two Republican presidential front-runners trading barbs over Social Security, illegal immigration and jobs.

Mr. Romney served up the opening salvo, questioning whether the Texas governor has walked away from previous statements in which he suggested Social Security is unconstitutional and should be returned to the states.

“There’s a Rick Perry out there that’s saying that it — almost to quote, it says that the federal government shouldn’t be in the pension business, that it’s unconstitutional, and it should be returned to the states,” Mr. Romney said. “So you’d better find that Rick Perry and get him to stop saying that.”

Mr. Perry responded by suggesting that Mr. Romney has waffled when it comes to the universal health care law he signed into law in 2006 as governor of Massachusetts.

“As a matter of fact, between books, your hard-copy book, you said that it was exactly what the American people needed to have — that’s ‘Romneycare’ — given to them as you had in Massachusetts,” Mr. Perry said. “Then in your paperback, you took that line out.”

Mr. Romney responded, “I actually wrote my book, and in my book I said no such thing.”

The two men also knocked heads over Mr. Perry’s decision to support in-state tuition for some children of illegal immigrants.

Mr. Romney said that the legislation carried a $100,000 price tag for Texas taxpayers and a “magnet” for illegal immigrants. Mr. Perry, however, refused to back off his support of the program, saying that anyone who doesn’t support it, “I don’t think you have a heart.”

“We need to be educating these people because they will become a drag on the society,” he said. “This was a state issue, Texas voted on it, and I still support it greatly.”

The Perry-Romney rumbles have turned into a traveling roadshow in recent weeks — with the Republicans standing side by side on debate stages and duking it out there and elsewhere on the campaign trail.

The feud has heated up as national polls have started to solidify, showing Mr. Perry and Mr. Romney running well ahead of the rest of the field, including Reps. Ron Paul of Texas and Michele Bachmann of Minnesota.

The Perry-Romney feud, which dominated the first segment of Thursday’s debate was a continuation of the day’s campaigning in this key swing state, with Mr. Romney telling the thousands gathered in a large ballroom for a Faith and Freedom Coalition rally that his background as “a conservative businessman” separates him from President Obama and his GOP rivals.

“There are plenty of people running for president who are politicians, and there’s nothing wrong with that,” he said, in what has become a go-to refrain for the former Massachusetts governor since Mr. Perry entered the race with a resume that includes more than 25 years in government.

“But to beat Barack Obama and to get America back on track to creating jobs and having a strong, stable foundation that will rebuild our economy, I think it helps to have someone who had a job to create jobs for the American people,” he said.

Mr. Perry later in the day played the populist card, calling himself the proud son of tenant farmers and the candidate of modest upbringing.

“I can tell you one thing. I wasn’t born with four aces in my hand,” Mr. Perry told the crowd, delivering a message that appears to be part of his campaign’s push to shine a light on Mr. Romney’s upbringing as a wealthy business scion. Mr. Romney’s father, George W. Romney, was chairman of American Motors Corp. and served as Michigan governor and in President Nixon’s Cabinet.

“We weren’t wealthy in material things, but we sure rich in a lot of other things. We were rich in spirit. We were rich in values,” Mr. Perry said of his family.

The comments also served as belated comeback to Mr. Romney’s suggestion that the strong job-growth numbers in Texas under Mr. Perry are the results of factors that for the most part are outside of Mr. Perry’s control; namely, a booming energy sector as well as the state’s lengthy history of low taxation and low regulation.

“If you’re dealt four aces, that doesn’t make you necessarily a great poker player,” Mr. Romney said.

The other candidates, meanwhile, hoped to make a splash and dislodge the “Perry vs. Romney” narrative that is driving national headlines. Recent history shows they have some reason for optimism.

In September 2007, former New York Mayor Rudolph W. Giuliani and former Sen. Fred Thompson of Tennessee were running ahead of Sen. John McCain of Arizona in the Republican nomination race, according to a Realclearpolitics.com average of national polls.

The field shrank by one Thursday after Rep. Thaddeus G. McCotter of Michigan dropped out of the race and endorsed Mr. Romney.

With that as a backdrop, the field used the Faith and Freedom rally at the Rosen Centre Hotel as a warm-up for the presidential debate. Mrs. Bachmann cast herself as a fighter and urged the Faith and Freedom crowd not to settle for a candidate who simply plays lip service to social conservatives.

“We need to have a candidate who is a true social conservative, who will stand for our issues,” she said.

Mr. Paul burnished his pro-life credentials, saying that all life must be protected. Former House Speaker Newt Gingrich said that he would sign executive orders eliminating all the administration’s “czar” positions and move the U.S. Embassy in Israel from Tel Aviv to Jerusalem.

Businessman Herman Cain said he would throw out the entire tax code and replace it with an across-the-board 9 percent tax of business, personal income and all sales. Former Sen. Rick Santorum of Pennsylvania said he was the “authentic” social conservative in the race.

The Romney camp started the tit-for-tat with Mr. Perry this week by issuing a press release that posed a handful of questions for Mr. Perry to answer regarding how Social Security would be transformed into a state-by-state program.

“Would states be free to forgo a pension program altogether?” the campaign asked. “If so, what if any provision would be made for the disabled and elderly in that state? Or would they be expected to move to other states with more generous benefits, inevitably overwhelming those systems?”

The Perry camp responded, saying that “Mr. Romney is again sounding like a Democrat, distorting the truth and trying to scare senior citizens.”

“As he has so many times in the past, Mr. Romney seems to forget he’s a Republican,” said Perry spokesman Ray Sullivan. “Mr. Romney has been running for president full time for nearly five years and has failed to issue a specific plan on Social Security. Rick Perry and other conservatives are courageous enough to be honest about federal spending and entitlements, whether Mr. Romney and the liberals like it or not.”

In an appearance on Fox News Channel on Wednesday, Mr. Perry personally repeated the line of attack.

“We need to nominate someone who has a stark, clear difference between the Republican nominee and President Obama,” he said. “We don’t need to nominate Obama-Lite.”

The two Republicans also traded blows on each other’s records on jobs, with the Romney camp contending the unemployment rate in Texas has doubled on Mr. Perry’s watch and the Perry camp pointing out that Massachusetts ranked 47th in job creation during Mr. Romney’s administration.